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Year: 2,011
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Edition: 4th
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Pages: 1,232
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Pages In File: 1,232
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Language: English
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Topic: 117
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Issue: 2011 12 30
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Identifier: 0073383112,9780073383118
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Ddc: 515/.22
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Lcc: QA353 .S649 2012
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Paginated: 1
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Org File Size: 92,398,798
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Extension: pdf
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Tags: Математика Математический анализ
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Toc: Cover......Page 1Title Page......Page 3Copyright......Page 4DEDICATION......Page 5Brief Table of Contents......Page 6Table of Contents......Page 8Seeing the Beauty and Power of Mathematics......Page 15Applications Index......Page 26CHAPTER 0 Preliminaries......Page 29The Real Number System and Inequalities......Page 30The Cartesian Plane......Page 34Equations of Lines......Page 37Functions......Page 400.3 Graphing Calculators and Computer Algebra Systems......Page 490.4 Trigonometric Functions......Page 550.5 Transformations of Functions......Page 641.1 A Brief Preview of Calculus: Tangent Lines and the Length of a Curve......Page 751.2 The Concept of Limit......Page 801.3 Computation of Limits......Page 871.4 Continuity and Its Consequences......Page 96The Method of Bisections......Page 1021.5 Limits Involving Infinity; Asymptotes......Page 106Limits at Infinity......Page 1091.6 Formal Definition of the Limit......Page 115Exploring the Definition of Limit Graphically......Page 119Limits Involving Infinity......Page 1211.7 Limits and Loss-of-Significance Errors......Page 126Computer Representation of Real Numbers......Page 1272.1 Tangent Lines and Velocity......Page 135The General Case......Page 137Velocity......Page 1392.2 The Derivative......Page 146Alternative Derivative Notations......Page 149Numerical Differentiation......Page 151The Power Rule......Page 155General Derivative Rules......Page 158Higher Order Derivatives......Page 159Acceleration......Page 160Product Rule......Page 163Quotient Rule......Page 165Applications......Page 1672.5 The Chain Rule......Page 1702.6 Derivatives of Trigonometric Functions......Page 175Applications......Page 1802.7 Implicit Differentiation......Page 1832.8 The Mean Value Theorem......Page 190CHAPTER 3 Applications of Differentiation......P